# How do you solve the inequality 8c-(c-5)>c+17?

Jan 21, 2017

See the entire solution process below:

#### Explanation:

First, combine like terms on the left side of the inequality:

$8 c - \left(c - 5\right) > c + 17$

$8 c - c + 5 > c + 17$

$7 c + 5 > c + 17$

Next, subtract $\textcolor{red}{c}$ and $\textcolor{b l u e}{5}$ from each side of the inequality to isolate the $c$ term while keeping the equation balanced:

$7 c + 5 - \textcolor{red}{c} - \textcolor{b l u e}{5} > c + 17 - \textcolor{red}{c} - \textcolor{b l u e}{5}$

$7 c - \textcolor{red}{c} + 5 - \textcolor{b l u e}{5} > c - \textcolor{red}{c} + 17 - \textcolor{b l u e}{5}$

$6 c + 0 > 0 + 17 - \textcolor{b l u e}{5}$

$6 c > 12$

Now, divide each side of the inequality by $\textcolor{red}{6}$ to solve for $c$ while keeping the inequality balanced:

$\frac{6 c}{\textcolor{red}{6}} > \frac{12}{\textcolor{red}{6}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} c}{\cancel{\textcolor{red}{6}}} > 2$

$c > 2$